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A229710 Least m of maximal order mod n such that m is a sum of two squares. 2
2, 5, 5, 5, 2, 13, 2, 5, 2, 5, 2, 5, 5, 5, 2, 13, 2, 13, 5, 5, 2, 37, 2, 5, 2, 13, 13, 5, 2, 5, 2, 5, 2, 13, 2, 13, 13, 5, 5, 13, 2, 5, 5, 5, 5, 13, 5, 37, 2, 5, 2, 5, 2, 37, 2, 13, 2, 13, 2, 5, 2, 5, 2, 5, 2, 17, 13, 5, 5, 5, 2, 13, 2, 37, 29, 13, 2, 13, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

COMMENTS

The sequence is undefined at n=4, as all the primitive roots are congruent to 3 mod 4.

Terms are not necessarily prime. For example, a(109) = 10.

a(prime(n)) = A229709(n).

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 5..10000

Christopher Ambrose, On the Least Primitive Root Expressible as a Sum of Two Squares, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A55, 2013.

EXAMPLE

The integer 5 = 2^2 + 1^2 has order 2 mod 12, the maximum, so a(12) = 5.

PROG

(Sage) def A229710(n) : m = Integers(n).unit_group_exponent(); return 0 if n==1 else next(i for i in PositiveIntegers() if mod(i, n).is_unit() and mod(i, n).multiplicative_order() == m and all(p%4 != 3 or e%2==0 for (p, e) in factor(i)))

CROSSREFS

Cf. A001481, A111076, A229708, A229709.

Sequence in context: A116698 A246900 A277086 * A240947 A023398 A186501

Adjacent sequences:  A229707 A229708 A229709 * A229711 A229712 A229713

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Sep 27 2013

STATUS

approved

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Last modified June 13 12:57 EDT 2021. Contains 344997 sequences. (Running on oeis4.)